# Properties

 Label 528d Number of curves 4 Conductor 528 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("528.i1")

sage: E.isogeny_class()

## Elliptic curves in class 528d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
528.i3 528d1 [0, 1, 0, -12, 12]  32 $$\Gamma_0(N)$$-optimal
528.i2 528d2 [0, 1, 0, -32, -60] [2, 2] 64
528.i1 528d3 [0, 1, 0, -472, -4108]  128
528.i4 528d4 [0, 1, 0, 88, -300]  128

## Rank

sage: E.rank()

The elliptic curves in class 528d have rank $$0$$.

## Modular form528.2.a.i

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} - q^{11} + 2q^{13} + 2q^{15} + 6q^{17} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 